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Spatial processes and Galois/concept lattices

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  • John Martin

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Abstract

There is a fair amount of interest in the use of Galois or Concept Lattices in the social sciences as a way of representing complex data structures; it does not seem to be widely appreciated that these structures are homologous to those arising from a discrete noncompensatory multidimensional response process, as originally outlined by Coombs. Here I formalize the spatial intuition underlying Coombs’s proposal, and show how, for any set of data, we may recreate the set of all possible minimal spatial representations. Copyright Springer Science+Business Media Dordrecht 2014

Suggested Citation

  • John Martin, 2014. "Spatial processes and Galois/concept lattices," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(2), pages 961-981, March.
  • Handle: RePEc:spr:qualqt:v:48:y:2014:i:2:p:961-981
    DOI: 10.1007/s11135-012-9818-9
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    References listed on IDEAS

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    1. Monjardet, Bernard, 2003. "The presence of lattice theory in discrete problems of mathematical social sciences. Why," Mathematical Social Sciences, Elsevier, vol. 46(2), pages 103-144, October.
    2. Susan Whitely, 1980. "Multicomponent latent trait models for ability tests," Psychometrika, Springer;The Psychometric Society, vol. 45(4), pages 479-494, December.
    3. Doignon, Jean-Paul & Falmagne, Jean-Claude, 1984. "Matching relations and the dimensional structure of social choices," Mathematical Social Sciences, Elsevier, vol. 7(3), pages 211-229, June.
    4. Michael Greenacre, 1988. "Clustering the rows and columns of a contingency table," Journal of Classification, Springer;The Classification Society, vol. 5(1), pages 39-51, March.
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